Special Issue Information

Dear Colleagues,

The journal Entropy is seeking papers for a Special Issue devoted to economics and finance (theory or empirical) in which information–theoretic entropy is the primary tool. Shannon entropy, Kullback–Leibler relative entropy, or other entropies (e.g., the Renyi or Tsallis entropies) should predominate. The entropies may be motivated by axiomatic rationale, frequentist rationale from the statistical theory of large deviations, or a more novel rationale. Moment-constrained entropy optimization may be used to produce Boltzmann–Gibbs type distributions applied in a variety of economic or finance settings. We emphasize that papers in which entropy plays a less central, more tangential role will be considered, but will not receive preference.

The underlying economics may be grounded in either micro- or macro-economics. Finance papers should also have some conventional grounding in finance theory, e.g., the arbitrage-free pricing of derivative securities enabled by a suitably moment-constrained entropy optimized risk-neutral distribution. Papers without such foundations, e.g., those metaphorically motivated by the natural sciences, will be considered at a secondary level. Our aim is to make this Special Issue more accessible to the mainstream economics and finance faculty, which by no means changes the desirable interdisciplinary scope of the regular issues of Entropy.

Please indicate on your submission that your paper is intended for the Special Issue on economic and finance applications.

Prof. Michael StutzerProf. Stelios BekirosGuest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

This paper systematically investigates the properties of six kinds of entropy-based risk measures: Information Entropy and Cumulative Residual Entropy in the probability space, Fuzzy Entropy, Credibility Entropy and Sine Entropy in the fuzzy space, and Hybrid Entropy in the hybridized uncertainty of both
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This paper systematically investigates the properties of six kinds of entropy-based risk measures: Information Entropy and Cumulative Residual Entropy in the probability space, Fuzzy Entropy, Credibility Entropy and Sine Entropy in the fuzzy space, and Hybrid Entropy in the hybridized uncertainty of both fuzziness and randomness. We discover that none of the risk measures satisfy all six of the following properties, which various scholars have associated with effective risk measures: Monotonicity, Translation Invariance, Sub-additivity, Positive Homogeneity, Consistency and Convexity. Measures based on Fuzzy Entropy, Credibility Entropy, and Sine Entropy all exhibit the same properties: Sub-additivity, Positive Homogeneity, Consistency, and Convexity. These measures based on Information Entropy and Hybrid Entropy, meanwhile, only exhibit Sub-additivity and Consistency. Cumulative Residual Entropy satisfies just Sub-additivity, Positive Homogeneity, and Convexity. After identifying these properties, we develop seven portfolio models based on different risk measures and made empirical comparisons using samples from both the Shenzhen Stock Exchange of China and the New York Stock Exchange of America. The comparisons show that the Mean Fuzzy Entropy Model performs the best among the seven models with respect to both daily returns and relative cumulative returns. Overall, these results could provide an important reference for both constructing effective risk measures and rationally selecting the appropriate risk measure under different portfolio selection conditions.
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Social science addresses systems in which the individual actions of participants interacting in complex, non-additive ways through institutional structures determine social outcomes. In many cases, the institutions incorporate enough negative feedback to stabilize the resulting outcome as an equilibrium. We study a particular
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Social science addresses systems in which the individual actions of participants interacting in complex, non-additive ways through institutional structures determine social outcomes. In many cases, the institutions incorporate enough negative feedback to stabilize the resulting outcome as an equilibrium. We study a particular type of such equilibria, quantal response statistical equilibrium (QRSE) using the tools of constrained maximum entropy modeling developed by E. T. Jaynes. We use Adam Smith’s theory of profit rate maximization through competition of freely mobile capitals as an example. Even in many cases where key model variables are unobserved, it is possible to infer the parameters characterizing the equilibrium through Bayesian methods. We apply this method to the Smithian theory of competition using data where firms’ profit rates are observed but the entry and exit decisions that determine the distribution of profit rates is unobserved, and confirm Smith’s prediction of the emergence of an average rate of profit, along with a characterization of equilibrium statistical fluctuations of individual rates of profit.
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The information-theoretical concept transfer entropy is an ideal measure for detecting conditional independence, or Granger causality in a time series setting. The recent literature indeed witnesses an increased interest in applications of entropy-based tests in this direction. However, those tests are typically based
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The information-theoretical concept transfer entropy is an ideal measure for detecting conditional independence, or Granger causality in a time series setting. The recent literature indeed witnesses an increased interest in applications of entropy-based tests in this direction. However, those tests are typically based on nonparametric entropy estimates for which the development of formal asymptotic theory turns out to be challenging. In this paper, we provide numerical comparisons for simulation-based tests to gain some insights into the statistical behavior of nonparametric transfer entropy-based tests. In particular, surrogate algorithms and smoothed bootstrap procedures are described and compared. We conclude this paper with a financial application to the detection of spillover effects in the global equity market.
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In this paper, we derive the optimal boundary for pair trading. This boundary defines the points of entry into or exit from the market for a given stock pair. However, if the assumed model contains uncertainty, the resulting boundary could result in large
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In this paper, we derive the optimal boundary for pair trading. This boundary defines the points of entry into or exit from the market for a given stock pair. However, if the assumed model contains uncertainty, the resulting boundary could result in large losses. To avoid this, we develop a more robust strategy by accounting for the model uncertainty. To incorporate the model uncertainty, we use the relative entropy as a penalty function in the expected profit from pair trading.
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An alternative derivation of the yield curve based on entropy or the loss of information as it is communicated through time is introduced. Given this focus on entropy growth in communication the Shannon entropy will be utilized. Additionally, Shannon entropy’s close relationship to
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An alternative derivation of the yield curve based on entropy or the loss of information as it is communicated through time is introduced. Given this focus on entropy growth in communication the Shannon entropy will be utilized. Additionally, Shannon entropy’s close relationship to the Kullback–Leibler divergence is used to provide a more precise understanding of this new yield curve. The derivation of the entropic yield curve is completed with the use of the Burnashev reliability function which serves as a weighting between the true and error distributions. The deep connections between the entropic yield curve and the popular Nelson–Siegel specification are also examined. Finally, this entropically derived yield curve is used to provide an estimate of the economy’s implied information processing ratio. This information theoretic ratio offers a new causal link between bond and equity markets, and is a valuable new tool for the modeling and prediction of stock market behavior.
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We study the structural correlations in the Italian overnight money market over the period 1999–2010. We show that the structural correlations vary across different versions of the network. Moreover, we employ different configuration models and examine whether higher-level characteristics of the observed network
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We study the structural correlations in the Italian overnight money market over the period 1999–2010. We show that the structural correlations vary across different versions of the network. Moreover, we employ different configuration models and examine whether higher-level characteristics of the observed network can be statistically reconstructed by maximizing the entropy of a randomized ensemble of networks restricted only by the lower-order features of the observed network. We find that often many of the high order correlations in the observed network can be considered emergent from the information embedded in the degree sequence in the binary version and in both the degree and strength sequences in the weighted version. However, this information is not enough to allow the models to account for all the patterns in the observed higher order structural correlations. In particular, one of the main features of the observed network that remains unexplained is the abnormally high level of weighted clustering in the years preceding the crisis, i.e., the huge increase in various indirect exposures generated via more intensive interbank credit links.
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This paper provides a comparative analysis of stock market dynamics of the 1987 and 2008 financial crises and discusses the extent to which risk management measures based on entropy can be successful in predicting aggregate market expectations. We find that the Tsallis entropy
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This paper provides a comparative analysis of stock market dynamics of the 1987 and 2008 financial crises and discusses the extent to which risk management measures based on entropy can be successful in predicting aggregate market expectations. We find that the Tsallis entropy is more appropriate for the short and sudden market crash of 1987, while the approximate entropy is the dominant predictor of the prolonged, fundamental crisis of 2008. We conclude by suggesting the use of entropy as a market sentiment indicator in technical analysis.
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Here, we consider the following inverse problem: Determination of an increasing continuous function U(x) on an interval [a,b] from the knowledge of the integrals ∫U(x)dFXi(x) [...] Read more.

Here, we consider the following inverse problem: Determination of an increasing continuous function U(x) on an interval [a,b] from the knowledge of the integrals ∫U(x)dFXi(x)=πi where the Xi are random variables taking values on [a,b] and πi are given numbers. This is a linear integral equation with discrete data, which can be transformed into a generalized moment problem when U(x) is supposed to have a positive derivative, and it becomes a classical interpolation problem if the Xi are deterministic. In some cases, e.g., in utility theory in economics, natural growth and convexity constraints are required on the function, which makes the inverse problem more interesting. Not only that, the data may be provided in intervals and/or measured up to an additive error. It is the purpose of this work to show how the standard method of maximum entropy, as well as the method of maximum entropy in the mean, provides an efficient method to deal with these problems.
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The Boltzmann–Gibbs (BG) entropy and its associated statistical mechanics were generalized, three decades ago, on the basis of the nonadditive entropy Sq (q∈R), which recovers the BG entropy in the q→1 limit. The optimization of S [...] Read more.

The Boltzmann–Gibbs (BG) entropy and its associated statistical mechanics were generalized, three decades ago, on the basis of the nonadditive entropy Sq (q∈R), which recovers the BG entropy in the q→1 limit. The optimization of Sq under appropriate simple constraints straightforwardly yields the so-called q-exponential and q-Gaussian distributions, respectively generalizing the exponential and Gaussian ones, recovered for q=1. These generalized functions ubiquitously emerge in complex systems, especially as economic and financial stylized features. These include price returns and volumes distributions, inter-occurrence times, characterization of wealth distributions and associated inequalities, among others. Here, we briefly review the basic concepts of this q-statistical generalization and focus on its rapidly growing applications in economics and finance.
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